That may be a bit tight. JetBlue international flights go into Terminal 4 (except for Nassau, which goes into 3). Customs at FLL, on average, takes about 35-45 minutes. Since you're not waiting for bags, it could be less. The Southwest departures are from Terminal 1. There is a shuttle on the lower level that goes from terminal to terminal or you can walk it in about 15 minutes (half that if, when you exit Terminal 4, you walk straight across the parking lot, to Terminal 1).
However, Southwest expects you to check in an hour in advance, and any delay on the JetBlue flight could present a problem. And, don't forget, you have to go through Security in Terminal 1, which can easily take 20-25 minutes. Even if Southwest closes the gate just 5 minutes before departure, you may not make it.